LMFDB - Embedded newform 8041.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8041,2,Mod(1,8041)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8041, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8041 = 11 \cdot 17 \cdot 43 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8041.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.2077082653$
Analytic rank:	$1$
Dimension:	$62$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	8041.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.99324 q^{2} +1.03243 q^{3} +1.97299 q^{4} -3.57518 q^{5} -2.05788 q^{6} +3.51904 q^{7} +0.0538292 q^{8} -1.93409 q^{9} +O(q^{10})$	\(q-1.99324 q^{2} +1.03243 q^{3} +1.97299 q^{4} -3.57518 q^{5} -2.05788 q^{6} +3.51904 q^{7} +0.0538292 q^{8} -1.93409 q^{9} +7.12618 q^{10} +1.00000 q^{11} +2.03698 q^{12} -5.52390 q^{13} -7.01428 q^{14} -3.69113 q^{15} -4.05328 q^{16} -1.00000 q^{17} +3.85509 q^{18} +2.09301 q^{19} -7.05381 q^{20} +3.63317 q^{21} -1.99324 q^{22} +2.06921 q^{23} +0.0555749 q^{24} +7.78190 q^{25} +11.0104 q^{26} -5.09410 q^{27} +6.94305 q^{28} +2.52600 q^{29} +7.35729 q^{30} +3.79764 q^{31} +7.97149 q^{32} +1.03243 q^{33} +1.99324 q^{34} -12.5812 q^{35} -3.81594 q^{36} +0.353684 q^{37} -4.17187 q^{38} -5.70305 q^{39} -0.192449 q^{40} +0.342632 q^{41} -7.24176 q^{42} +1.00000 q^{43} +1.97299 q^{44} +6.91470 q^{45} -4.12442 q^{46} -12.5093 q^{47} -4.18473 q^{48} +5.38365 q^{49} -15.5112 q^{50} -1.03243 q^{51} -10.8986 q^{52} +9.31641 q^{53} +10.1538 q^{54} -3.57518 q^{55} +0.189427 q^{56} +2.16089 q^{57} -5.03491 q^{58} -3.44167 q^{59} -7.28257 q^{60} -1.44272 q^{61} -7.56960 q^{62} -6.80613 q^{63} -7.78251 q^{64} +19.7489 q^{65} -2.05788 q^{66} +5.59658 q^{67} -1.97299 q^{68} +2.13631 q^{69} +25.0773 q^{70} -0.575712 q^{71} -0.104110 q^{72} +4.71069 q^{73} -0.704977 q^{74} +8.03428 q^{75} +4.12950 q^{76} +3.51904 q^{77} +11.3675 q^{78} +0.0981581 q^{79} +14.4912 q^{80} +0.542949 q^{81} -0.682946 q^{82} +11.2845 q^{83} +7.16822 q^{84} +3.57518 q^{85} -1.99324 q^{86} +2.60792 q^{87} +0.0538292 q^{88} +4.37303 q^{89} -13.7826 q^{90} -19.4388 q^{91} +4.08253 q^{92} +3.92080 q^{93} +24.9341 q^{94} -7.48289 q^{95} +8.23002 q^{96} +14.3739 q^{97} -10.7309 q^{98} -1.93409 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) $ 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.99324	−1.40943	−0.704716	−	0.709490i	$-0.748925\pi$
$2$	−1.99324	−1.40943	−0.704716	+	0.709490i	$0.748925\pi$
$3$	1.03243	0.596074	0.298037	−	0.954554i	$-0.403668\pi$
$3$	1.03243	0.596074	0.298037	+	0.954554i	$0.403668\pi$
$4$	1.97299	0.986497
$5$	−3.57518	−1.59887	−0.799434	−	0.600754i	$-0.794867\pi$
$5$	−3.57518	−1.59887	−0.799434	+	0.600754i	$0.794867\pi$
$6$	−2.05788	−0.840126
$7$	3.51904	1.33007	0.665036	−	0.746811i	$-0.268416\pi$
$7$	3.51904	1.33007	0.665036	+	0.746811i	$0.268416\pi$
$8$	0.0538292	0.0190315
$9$	−1.93409	−0.644695
$10$	7.12618	2.25350
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	2.03698	0.588026
$13$	−5.52390	−1.53205	−0.766027	−	0.642808i	$-0.777769\pi$
$13$	−5.52390	−1.53205	−0.766027	+	0.642808i	$0.777769\pi$
$14$	−7.01428	−1.87465
$15$	−3.69113	−0.953044
$16$	−4.05328	−1.01332
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	3.85509	0.908654
$19$	2.09301	0.480170	0.240085	−	0.970752i	$-0.422825\pi$
$19$	2.09301	0.480170	0.240085	+	0.970752i	$0.422825\pi$
$20$	−7.05381	−1.57728
$21$	3.63317	0.792822
$22$	−1.99324	−0.424960
$23$	2.06921	0.431459	0.215730	−	0.976453i	$-0.430787\pi$
$23$	2.06921	0.431459	0.215730	+	0.976453i	$0.430787\pi$
$24$	0.0555749	0.0113442
$25$	7.78190	1.55638
$26$	11.0104	2.15933
$27$	−5.09410	−0.980361
$28$	6.94305	1.31211
$29$	2.52600	0.469066	0.234533	−	0.972108i	$-0.424644\pi$
$29$	2.52600	0.469066	0.234533	+	0.972108i	$0.424644\pi$
$30$	7.35729	1.34325
$31$	3.79764	0.682077	0.341038	−	0.940049i	$-0.389221\pi$
$31$	3.79764	0.682077	0.341038	+	0.940049i	$0.389221\pi$
$32$	7.97149	1.40917
$33$	1.03243	0.179723
$34$	1.99324	0.341837
$35$	−12.5812	−2.12661
$36$	−3.81594	−0.635990
$37$	0.353684	0.0581453	0.0290727	−	0.999577i	$-0.490745\pi$
$37$	0.353684	0.0581453	0.0290727	+	0.999577i	$0.490745\pi$
$38$	−4.17187	−0.676767
$39$	−5.70305	−0.913218
$40$	−0.192449	−0.0304289
$41$	0.342632	0.0535101	0.0267550	−	0.999642i	$-0.491483\pi$
$41$	0.342632	0.0535101	0.0267550	+	0.999642i	$0.491483\pi$
$42$	−7.24176	−1.11743
$43$	1.00000	0.152499
$43$	1.00000	0.152499
$44$	1.97299	0.297440
$45$	6.91470	1.03078
$46$	−4.12442	−0.608112
$47$	−12.5093	−1.82467	−0.912337	−	0.409440i	$-0.865724\pi$
$47$	−12.5093	−1.82467	−0.912337	+	0.409440i	$0.865724\pi$
$48$	−4.18473	−0.604014
$49$	5.38365	0.769093
$50$	−15.5112	−2.19361
$51$	−1.03243	−0.144569
$52$	−10.8986	−1.51137
$53$	9.31641	1.27971	0.639853	−	0.768497i	$-0.278995\pi$
$53$	9.31641	1.27971	0.639853	+	0.768497i	$0.278995\pi$
$54$	10.1538	1.38175
$55$	−3.57518	−0.482077
$56$	0.189427	0.0253133
$57$	2.16089	0.286217
$58$	−5.03491	−0.661117
$59$	−3.44167	−0.448067	−0.224034	−	0.974581i	$-0.571923\pi$
$59$	−3.44167	−0.448067	−0.224034	+	0.974581i	$0.571923\pi$
$60$	−7.28257	−0.940176
$61$	−1.44272	−0.184721	−0.0923604	−	0.995726i	$-0.529441\pi$
$61$	−1.44272	−0.184721	−0.0923604	+	0.995726i	$0.529441\pi$
$62$	−7.56960	−0.961340
$63$	−6.80613	−0.857492
$64$	−7.78251	−0.972814
$65$	19.7489	2.44955
$66$	−2.05788	−0.253307
$67$	5.59658	0.683731	0.341865	−	0.939749i	$-0.388941\pi$
$67$	5.59658	0.683731	0.341865	+	0.939749i	$0.388941\pi$
$68$	−1.97299	−0.239261
$69$	2.13631	0.257182
$70$	25.0773	2.99731
$71$	−0.575712	−0.0683245	−0.0341622	−	0.999416i	$-0.510876\pi$
$71$	−0.575712	−0.0683245	−0.0341622	+	0.999416i	$0.510876\pi$
$72$	−0.104110	−0.0122695
$73$	4.71069	0.551345	0.275672	−	0.961252i	$-0.411100\pi$
$73$	4.71069	0.551345	0.275672	+	0.961252i	$0.411100\pi$
$74$	−0.704977	−0.0819519
$75$	8.03428	0.927719
$76$	4.12950	0.473686
$77$	3.51904	0.401032
$78$	11.3675	1.28712
$79$	0.0981581	0.0110436	0.00552182	−	0.999985i	$-0.498242\pi$
$79$	0.0981581	0.0110436	0.00552182	+	0.999985i	$0.498242\pi$
$80$	14.4912	1.62017
$81$	0.542949	0.0603276
$82$	−0.682946	−0.0754188
$83$	11.2845	1.23863	0.619317	−	0.785141i	$-0.287410\pi$
$83$	11.2845	1.23863	0.619317	+	0.785141i	$0.287410\pi$
$84$	7.16822	0.782117
$85$	3.57518	0.387783
$86$	−1.99324	−0.214936
$87$	2.60792	0.279598
$88$	0.0538292	0.00573821
$89$	4.37303	0.463540	0.231770	−	0.972771i	$-0.425548\pi$
$89$	4.37303	0.463540	0.231770	+	0.972771i	$0.425548\pi$
$90$	−13.7826	−1.45282
$91$	−19.4388	−2.03774
$92$	4.08253	0.425633
$93$	3.92080	0.406568
$94$	24.9341	2.57175
$95$	−7.48289	−0.767729
$96$	8.23002	0.839973
$97$	14.3739	1.45945	0.729725	−	0.683741i	$-0.239648\pi$
$97$	14.3739	1.45945	0.729725	+	0.683741i	$0.239648\pi$
$98$	−10.7309	−1.08398
$99$	−1.93409	−0.194383
$100$	15.3537	1.53537
$101$	−7.08553	−0.705037	−0.352518	−	0.935805i	$-0.614675\pi$
$101$	−7.08553	−0.705037	−0.352518	+	0.935805i	$0.614675\pi$
$102$	2.05788	0.203760
$103$	4.60019	0.453270	0.226635	−	0.973980i	$-0.427228\pi$
$103$	4.60019	0.453270	0.226635	+	0.973980i	$0.427228\pi$
$104$	−0.297347	−0.0291573
$105$	−12.9892	−1.26762
$106$	−18.5698	−1.80366
$107$	−14.2829	−1.38078	−0.690389	−	0.723439i	$-0.742560\pi$
$107$	−14.2829	−1.38078	−0.690389	+	0.723439i	$0.742560\pi$
$108$	−10.0506	−0.967123
$109$	4.44136	0.425405	0.212702	−	0.977117i	$-0.431773\pi$
$109$	4.44136	0.425405	0.212702	+	0.977117i	$0.431773\pi$
$110$	7.12618	0.679455
$111$	0.365155	0.0346589
$112$	−14.2637	−1.34779
$113$	−5.98156	−0.562698	−0.281349	−	0.959606i	$-0.590782\pi$
$113$	−5.98156	−0.562698	−0.281349	+	0.959606i	$0.590782\pi$
$114$	−4.30717	−0.403403
$115$	−7.39778	−0.689846
$116$	4.98378	0.462732
$117$	10.6837	0.987708
$118$	6.86006	0.631520
$119$	−3.51904	−0.322590
$120$	−0.198690	−0.0181379
$121$	1.00000	0.0909091
$122$	2.87567	0.260351
$123$	0.353744	0.0318960
$124$	7.49272	0.672866
$125$	−9.94580	−0.889580
$126$	13.5662	1.20858
$127$	−14.6534	−1.30028	−0.650138	−	0.759816i	$-0.725289\pi$
$127$	−14.6534	−1.30028	−0.650138	+	0.759816i	$0.725289\pi$
$128$	−0.430594	−0.0380595
$129$	1.03243	0.0909005
$130$	−39.3643	−3.45248
$131$	−9.44765	−0.825445	−0.412723	−	0.910857i	$-0.635422\pi$
$131$	−9.44765	−0.825445	−0.412723	+	0.910857i	$0.635422\pi$
$132$	2.03698	0.177296
$133$	7.36540	0.638661
$134$	−11.1553	−0.963671
$135$	18.2123	1.56747
$136$	−0.0538292	−0.00461582
$137$	−2.26115	−0.193183	−0.0965915	−	0.995324i	$-0.530794\pi$
$137$	−2.26115	−0.193183	−0.0965915	+	0.995324i	$0.530794\pi$
$138$	−4.25818	−0.362480
$139$	6.77562	0.574700	0.287350	−	0.957826i	$-0.407226\pi$
$139$	6.77562	0.574700	0.287350	+	0.957826i	$0.407226\pi$
$140$	−24.8226	−2.09790
$141$	−12.9150	−1.08764
$142$	1.14753	0.0962987
$143$	−5.52390	−0.461932
$144$	7.83940	0.653283
$145$	−9.03090	−0.749975
$146$	−9.38952	−0.777083
$147$	5.55825	0.458436
$148$	0.697817	0.0573602
$149$	−17.1288	−1.40325	−0.701623	−	0.712548i	$-0.747541\pi$
$149$	−17.1288	−1.40325	−0.701623	+	0.712548i	$0.747541\pi$
$150$	−16.0142	−1.30756
$151$	6.31799	0.514151	0.257075	−	0.966391i	$-0.417241\pi$
$151$	6.31799	0.514151	0.257075	+	0.966391i	$0.417241\pi$
$152$	0.112665	0.00913835
$153$	1.93409	0.156362
$154$	−7.01428	−0.565227
$155$	−13.5772	−1.09055
$156$	−11.2521	−0.900887
$157$	22.4225	1.78951	0.894754	−	0.446559i	$-0.147351\pi$
$157$	22.4225	1.78951	0.894754	+	0.446559i	$0.147351\pi$
$158$	−0.195652	−0.0155653
$159$	9.61855	0.762800
$160$	−28.4995	−2.25308
$161$	7.28162	0.573872
$162$	−1.08223	−0.0850276
$163$	−4.40254	−0.344833	−0.172417	−	0.985024i	$-0.555158\pi$
$163$	−4.40254	−0.344833	−0.172417	+	0.985024i	$0.555158\pi$
$164$	0.676010	0.0527875
$165$	−3.69113	−0.287354
$166$	−22.4927	−1.74577
$167$	−21.7483	−1.68293	−0.841467	−	0.540309i	$-0.818307\pi$
$167$	−21.7483	−1.68293	−0.841467	+	0.540309i	$0.818307\pi$
$168$	0.195570	0.0150886
$169$	17.5135	1.34719
$170$	−7.12618	−0.546553
$171$	−4.04807	−0.309563
$172$	1.97299	0.150439
$173$	−9.45344	−0.718732	−0.359366	−	0.933197i	$-0.617007\pi$
$173$	−9.45344	−0.718732	−0.359366	+	0.933197i	$0.617007\pi$
$174$	−5.19820	−0.394075
$175$	27.3848	2.07010
$176$	−4.05328	−0.305528
$177$	−3.55329	−0.267081
$178$	−8.71648	−0.653328
$179$	−21.6098	−1.61519	−0.807597	−	0.589734i	$-0.799232\pi$
$179$	−21.6098	−1.61519	−0.807597	+	0.589734i	$0.799232\pi$
$180$	13.6427	1.01686
$181$	−0.756738	−0.0562479	−0.0281239	−	0.999604i	$-0.508953\pi$
$181$	−0.756738	−0.0562479	−0.0281239	+	0.999604i	$0.508953\pi$
$182$	38.7462	2.87206
$183$	−1.48950	−0.110107
$184$	0.111384	0.00821131
$185$	−1.26448	−0.0929668
$186$	−7.81509	−0.573030
$187$	−1.00000	−0.0731272
$188$	−24.6808	−1.80004
$189$	−17.9264	−1.30395
$190$	14.9152	1.08206
$191$	−5.90351	−0.427163	−0.213581	−	0.976925i	$-0.568513\pi$
$191$	−5.90351	−0.427163	−0.213581	+	0.976925i	$0.568513\pi$
$192$	−8.03491	−0.579870
$193$	1.77096	0.127476	0.0637382	−	0.997967i	$-0.479698\pi$
$193$	1.77096	0.127476	0.0637382	+	0.997967i	$0.479698\pi$
$194$	−28.6506	−2.05699
$195$	20.3894	1.46012
$196$	10.6219	0.758708
$197$	7.04793	0.502144	0.251072	−	0.967968i	$-0.419217\pi$
$197$	7.04793	0.502144	0.251072	+	0.967968i	$0.419217\pi$
$198$	3.85509	0.273969
$199$	3.38230	0.239765	0.119882	−	0.992788i	$-0.461748\pi$
$199$	3.38230	0.239765	0.119882	+	0.992788i	$0.461748\pi$
$200$	0.418894	0.0296203
$201$	5.77808	0.407554
$202$	14.1231	0.993701
$203$	8.88909	0.623892
$204$	−2.03698	−0.142617
$205$	−1.22497	−0.0855556
$206$	−9.16926	−0.638853
$207$	−4.00202	−0.278160
$208$	22.3899	1.55246
$209$	2.09301	0.144777
$210$	25.8906	1.78662
$211$	−21.5211	−1.48158	−0.740788	−	0.671739i	$-0.765548\pi$
$211$	−21.5211	−1.48158	−0.740788	+	0.671739i	$0.765548\pi$
$212$	18.3812	1.26243
$213$	−0.594383	−0.0407265
$214$	28.4691	1.94611
$215$	−3.57518	−0.243825
$216$	−0.274212	−0.0186577
$217$	13.3641	0.907211
$218$	−8.85268	−0.599579
$219$	4.86346	0.328642
$220$	−7.05381	−0.475568
$221$	5.52390	0.371578
$222$	−0.727840	−0.0488494
$223$	−8.50657	−0.569642	−0.284821	−	0.958581i	$-0.591934\pi$
$223$	−8.50657	−0.569642	−0.284821	+	0.958581i	$0.591934\pi$
$224$	28.0520	1.87430
$225$	−15.0509	−1.00339
$226$	11.9227	0.793084
$227$	16.4932	1.09469	0.547346	−	0.836906i	$-0.315638\pi$
$227$	16.4932	1.09469	0.547346	+	0.836906i	$0.315638\pi$
$228$	4.26343	0.282352
$229$	17.3654	1.14754	0.573769	−	0.819017i	$-0.305481\pi$
$229$	17.3654	1.14754	0.573769	+	0.819017i	$0.305481\pi$
$230$	14.7455	0.972291
$231$	3.63317	0.239045
$232$	0.135973	0.00892703
$233$	16.0968	1.05453	0.527267	−	0.849700i	$-0.323217\pi$
$233$	16.0968	1.05453	0.527267	+	0.849700i	$0.323217\pi$
$234$	−21.2951	−1.39211
$235$	44.7231	2.91741
$236$	−6.79039	−0.442017
$237$	0.101341	0.00658283
$238$	7.01428	0.454668
$239$	−11.2863	−0.730052	−0.365026	−	0.930997i	$-0.618940\pi$
$239$	−11.2863	−0.730052	−0.365026	+	0.930997i	$0.618940\pi$
$240$	14.9612	0.965740
$241$	8.54234	0.550260	0.275130	−	0.961407i	$-0.411279\pi$
$241$	8.54234	0.550260	0.275130	+	0.961407i	$0.411279\pi$
$242$	−1.99324	−0.128130
$243$	15.8429	1.01632
$244$	−2.84647	−0.182227
$245$	−19.2475	−1.22968
$246$	−0.705095	−0.0449552
$247$	−11.5616	−0.735647
$248$	0.204424	0.0129809
$249$	11.6505	0.738317
$250$	19.8243	1.25380
$251$	18.6056	1.17437	0.587186	−	0.809452i	$-0.300236\pi$
$251$	18.6056	1.17437	0.587186	+	0.809452i	$0.300236\pi$
$252$	−13.4285	−0.845913
$253$	2.06921	0.130090
$254$	29.2076	1.83265
$255$	3.69113	0.231147
$256$	16.4233	1.02646
$257$	−23.4073	−1.46011	−0.730053	−	0.683390i	$-0.760505\pi$
$257$	−23.4073	−1.46011	−0.730053	+	0.683390i	$0.760505\pi$
$258$	−2.05788	−0.128118
$259$	1.24463	0.0773375
$260$	38.9645	2.41648
$261$	−4.88550	−0.302405
$262$	18.8314	1.16341
$263$	−9.75028	−0.601228	−0.300614	−	0.953746i	$-0.597192\pi$
$263$	−9.75028	−0.601228	−0.300614	+	0.953746i	$0.597192\pi$
$264$	0.0555749	0.00342040
$265$	−33.3078	−2.04608
$266$	−14.6810	−0.900149
$267$	4.51485	0.276304
$268$	11.0420	0.674498
$269$	20.0603	1.22310	0.611548	−	0.791208i	$-0.290547\pi$
$269$	20.0603	1.22310	0.611548	+	0.791208i	$0.290547\pi$
$270$	−36.3015	−2.20924
$271$	−10.1880	−0.618879	−0.309439	−	0.950919i	$-0.600141\pi$
$271$	−10.1880	−0.618879	−0.309439	+	0.950919i	$0.600141\pi$
$272$	4.05328	0.245766
$273$	−20.0693	−1.21465
$274$	4.50701	0.272278
$275$	7.78190	0.469266
$276$	4.21493	0.253709
$277$	6.90016	0.414590	0.207295	−	0.978278i	$-0.433534\pi$
$277$	6.90016	0.414590	0.207295	+	0.978278i	$0.433534\pi$
$278$	−13.5054	−0.810001
$279$	−7.34497	−0.439732
$280$	−0.677236	−0.0404726
$281$	−8.64750	−0.515867	−0.257933	−	0.966163i	$-0.583042\pi$
$281$	−8.64750	−0.515867	−0.257933	+	0.966163i	$0.583042\pi$
$282$	25.7427	1.53296
$283$	26.8922	1.59858	0.799288	−	0.600948i	$-0.205210\pi$
$283$	26.8922	1.59858	0.799288	+	0.600948i	$0.205210\pi$
$284$	−1.13588	−0.0674019
$285$	−7.72557	−0.457623
$286$	11.0104	0.651061
$287$	1.20573	0.0711723
$288$	−15.4176	−0.908488
$289$	1.00000	0.0588235
$290$	18.0007	1.05704
$291$	14.8401	0.869940
$292$	9.29417	0.543900
$293$	−10.8418	−0.633383	−0.316691	−	0.948529i	$-0.602572\pi$
$293$	−10.8418	−0.633383	−0.316691	+	0.948529i	$0.602572\pi$
$294$	−11.0789	−0.646135
$295$	12.3046	0.716400
$296$	0.0190385	0.00110659
$297$	−5.09410	−0.295590
$298$	34.1418	1.97778
$299$	−11.4301	−0.661019
$300$	15.8516	0.915192
$301$	3.51904	0.202834
$302$	−12.5933	−0.724661
$303$	−7.31532	−0.420254
$304$	−8.48357	−0.486566
$305$	5.15797	0.295344
$306$	−3.85509	−0.220381
$307$	−8.28714	−0.472972	−0.236486	−	0.971635i	$-0.575996\pi$
$307$	−8.28714	−0.472972	−0.236486	+	0.971635i	$0.575996\pi$
$308$	6.94305	0.395617
$309$	4.74938	0.270183
$310$	27.0627	1.53706
$311$	−5.75262	−0.326201	−0.163101	−	0.986609i	$-0.552150\pi$
$311$	−5.75262	−0.326201	−0.163101	+	0.986609i	$0.552150\pi$
$312$	−0.306990	−0.0173799
$313$	−31.6383	−1.78830	−0.894152	−	0.447764i	$-0.852221\pi$
$313$	−31.6383	−1.78830	−0.894152	+	0.447764i	$0.852221\pi$
$314$	−44.6933	−2.52219
$315$	24.3331	1.37102
$316$	0.193665	0.0108945
$317$	16.2515	0.912773	0.456386	−	0.889782i	$-0.349144\pi$
$317$	16.2515	0.912773	0.456386	+	0.889782i	$0.349144\pi$
$318$	−19.1720	−1.07511
$319$	2.52600	0.141429
$320$	27.8239	1.55540
$321$	−14.7461	−0.823046
$322$	−14.5140	−0.808833
$323$	−2.09301	−0.116458
$324$	1.07123	0.0595130
$325$	−42.9865	−2.38446
$326$	8.77530	0.486019
$327$	4.58540	0.253573
$328$	0.0184436	0.00101838
$329$	−44.0209	−2.42695
$330$	7.35729	0.405005
$331$	−2.96993	−0.163242	−0.0816211	−	0.996663i	$-0.526010\pi$
$331$	−2.96993	−0.163242	−0.0816211	+	0.996663i	$0.526010\pi$
$332$	22.2642	1.22191
$333$	−0.684056	−0.0374860
$334$	43.3495	2.37198
$335$	−20.0088	−1.09320
$336$	−14.7263	−0.803383
$337$	1.76375	0.0960777	0.0480388	−	0.998845i	$-0.484703\pi$
$337$	1.76375	0.0960777	0.0480388	+	0.998845i	$0.484703\pi$
$338$	−34.9085	−1.89877
$339$	−6.17555	−0.335410
$340$	7.05381	0.382546
$341$	3.79764	0.205654
$342$	8.06876	0.436308
$343$	−5.68801	−0.307124
$344$	0.0538292	0.00290228
$345$	−7.63770	−0.411200
$346$	18.8429	1.01300
$347$	4.58744	0.246267	0.123133	−	0.992390i	$-0.460706\pi$
$347$	4.58744	0.246267	0.123133	+	0.992390i	$0.460706\pi$
$348$	5.14541	0.275823
$349$	4.23495	0.226692	0.113346	−	0.993556i	$-0.463843\pi$
$349$	4.23495	0.226692	0.113346	+	0.993556i	$0.463843\pi$
$350$	−54.5845	−2.91766
$351$	28.1393	1.50197
$352$	7.97149	0.424882
$353$	−12.4763	−0.664046	−0.332023	−	0.943271i	$-0.607731\pi$
$353$	−12.4763	−0.664046	−0.332023	+	0.943271i	$0.607731\pi$
$354$	7.08254	0.376433
$355$	2.05827	0.109242
$356$	8.62796	0.457281
$357$	−3.63317	−0.192288
$358$	43.0735	2.27651
$359$	8.03412	0.424024	0.212012	−	0.977267i	$-0.431998\pi$
$359$	8.03412	0.424024	0.212012	+	0.977267i	$0.431998\pi$
$360$	0.372213	0.0196173
$361$	−14.6193	−0.769437
$362$	1.50836	0.0792775
$363$	1.03243	0.0541886
$364$	−38.3527	−2.01023
$365$	−16.8416	−0.881528
$366$	2.96894	0.155189
$367$	−21.4557	−1.11998	−0.559990	−	0.828499i	$-0.689195\pi$
$367$	−21.4557	−1.11998	−0.559990	+	0.828499i	$0.689195\pi$
$368$	−8.38707	−0.437206
$369$	−0.662679	−0.0344977
$370$	2.52042	0.131030
$371$	32.7848	1.70210
$372$	7.73572	0.401078
$373$	−6.53863	−0.338557	−0.169279	−	0.985568i	$-0.554144\pi$
$373$	−6.53863	−0.338557	−0.169279	+	0.985568i	$0.554144\pi$
$374$	1.99324	0.103068
$375$	−10.2684	−0.530256
$376$	−0.673368	−0.0347263
$377$	−13.9534	−0.718635
$378$	35.7315	1.83783
$379$	−8.80740	−0.452406	−0.226203	−	0.974080i	$-0.572631\pi$
$379$	−8.80740	−0.452406	−0.226203	+	0.974080i	$0.572631\pi$
$380$	−14.7637	−0.757362
$381$	−15.1286	−0.775061
$382$	11.7671	0.602057
$383$	−37.1089	−1.89618	−0.948088	−	0.318007i	$-0.896987\pi$
$383$	−37.1089	−1.89618	−0.948088	+	0.318007i	$0.896987\pi$
$384$	−0.444559	−0.0226863
$385$	−12.5812	−0.641197
$386$	−3.52994	−0.179669
$387$	−1.93409	−0.0983151
$388$	28.3596	1.43974
$389$	13.7647	0.697896	0.348948	−	0.937142i	$-0.386539\pi$
$389$	13.7647	0.697896	0.348948	+	0.937142i	$0.386539\pi$
$390$	−40.6409	−2.05793
$391$	−2.06921	−0.104644
$392$	0.289797	0.0146370
$393$	−9.75405	−0.492027
$394$	−14.0482	−0.707738
$395$	−0.350933	−0.0176573
$396$	−3.81594	−0.191758
$397$	13.3156	0.668289	0.334145	−	0.942522i	$-0.391553\pi$
$397$	13.3156	0.668289	0.334145	+	0.942522i	$0.391553\pi$
$398$	−6.74173	−0.337932
$399$	7.60426	0.380689
$400$	−31.5423	−1.57711
$401$	18.8190	0.939776	0.469888	−	0.882726i	$-0.344294\pi$
$401$	18.8190	0.939776	0.469888	+	0.882726i	$0.344294\pi$
$402$	−11.5171	−0.574420
$403$	−20.9778	−1.04498
$404$	−13.9797	−0.695517
$405$	−1.94114	−0.0964559
$406$	−17.7181	−0.879333
$407$	0.353684	0.0175315
$408$	−0.0555749	−0.00275137
$409$	30.6421	1.51515	0.757576	−	0.652747i	$-0.226383\pi$
$409$	30.6421	1.51515	0.757576	+	0.652747i	$0.226383\pi$
$410$	2.44165	0.120585
$411$	−2.33448	−0.115151
$412$	9.07614	0.447149
$413$	−12.1114	−0.595962
$414$	7.97698	0.392047
$415$	−40.3441	−1.98041
$416$	−44.0337	−2.15893
$417$	6.99536	0.342564
$418$	−4.17187	−0.204053
$419$	17.7613	0.867697	0.433849	−	0.900986i	$-0.357155\pi$
$419$	17.7613	0.867697	0.433849	+	0.900986i	$0.357155\pi$
$420$	−25.6277	−1.25050
$421$	6.56016	0.319723	0.159861	−	0.987139i	$-0.448895\pi$
$421$	6.56016	0.319723	0.159861	+	0.987139i	$0.448895\pi$
$422$	42.8967	2.08818
$423$	24.1941	1.17636
$424$	0.501495	0.0243547
$425$	−7.78190	−0.377478
$426$	1.18475	0.0574012
$427$	−5.07698	−0.245692
$428$	−28.1800	−1.36213
$429$	−5.70305	−0.275346
$430$	7.12618	0.343655
$431$	7.59466	0.365822	0.182911	−	0.983129i	$-0.441448\pi$
$431$	7.59466	0.365822	0.182911	+	0.983129i	$0.441448\pi$
$432$	20.6478	0.993420
$433$	−18.0561	−0.867723	−0.433861	−	0.900980i	$-0.642849\pi$
$433$	−18.0561	−0.867723	−0.433861	+	0.900980i	$0.642849\pi$
$434$	−26.6377	−1.27865
$435$	−9.32378	−0.447041
$436$	8.76277	0.419661
$437$	4.33087	0.207174
$438$	−9.69404	−0.463199
$439$	1.14060	0.0544377	0.0272188	−	0.999629i	$-0.491335\pi$
$439$	1.14060	0.0544377	0.0272188	+	0.999629i	$0.491335\pi$
$440$	−0.192449	−0.00917465
$441$	−10.4124	−0.495830
$442$	−11.0104	−0.523713
$443$	8.96002	0.425703	0.212852	−	0.977085i	$-0.431725\pi$
$443$	8.96002	0.425703	0.212852	+	0.977085i	$0.431725\pi$
$444$	0.720448	0.0341909
$445$	−15.6344	−0.741140
$446$	16.9556	0.802872
$447$	−17.6843	−0.836439
$448$	−27.3870	−1.29391
$449$	−29.1127	−1.37391	−0.686956	−	0.726699i	$-0.741053\pi$
$449$	−29.1127	−1.37391	−0.686956	+	0.726699i	$0.741053\pi$
$450$	30.0000	1.41421
$451$	0.342632	0.0161339
$452$	−11.8016	−0.555100
$453$	6.52289	0.306472
$454$	−32.8749	−1.54289
$455$	69.4973	3.25808
$456$	0.116319	0.00544714
$457$	39.1103	1.82950	0.914751	−	0.404019i	$-0.132387\pi$
$457$	39.1103	1.82950	0.914751	+	0.404019i	$0.132387\pi$
$458$	−34.6133	−1.61737
$459$	5.09410	0.237772
$460$	−14.5958	−0.680531
$461$	4.16153	0.193822	0.0969109	−	0.995293i	$-0.469104\pi$
$461$	4.16153	0.193822	0.0969109	+	0.995293i	$0.469104\pi$
$462$	−7.24176	−0.336917
$463$	−12.6559	−0.588171	−0.294085	−	0.955779i	$-0.595015\pi$
$463$	−12.6559	−0.588171	−0.294085	+	0.955779i	$0.595015\pi$
$464$	−10.2386	−0.475314
$465$	−14.0176	−0.650049
$466$	−32.0847	−1.48629
$467$	−12.7906	−0.591878	−0.295939	−	0.955207i	$-0.595633\pi$
$467$	−12.7906	−0.591878	−0.295939	+	0.955207i	$0.595633\pi$
$468$	21.0789	0.974371
$469$	19.6946	0.909411
$470$	−89.1438	−4.11190
$471$	23.1497	1.06668
$472$	−0.185262	−0.00852739
$473$	1.00000	0.0459800
$474$	−0.201997	−0.00927805
$475$	16.2876	0.747327
$476$	−6.94305	−0.318234
$477$	−18.0187	−0.825021
$478$	22.4963	1.02896
$479$	−11.8557	−0.541703	−0.270851	−	0.962621i	$-0.587305\pi$
$479$	−11.8557	−0.541703	−0.270851	+	0.962621i	$0.587305\pi$
$480$	−29.4238	−1.34301
$481$	−1.95372	−0.0890818
$482$	−17.0269	−0.775554
$483$	7.51777	0.342070
$484$	1.97299	0.0896815
$485$	−51.3893	−2.33347
$486$	−31.5786	−1.43243
$487$	−15.6618	−0.709702	−0.354851	−	0.934923i	$-0.615468\pi$
$487$	−15.6618	−0.709702	−0.354851	+	0.934923i	$0.615468\pi$
$488$	−0.0776602	−0.00351551
$489$	−4.54532	−0.205546
$490$	38.3648	1.73315
$491$	−33.3135	−1.50342	−0.751709	−	0.659495i	$-0.770770\pi$
$491$	−33.3135	−1.50342	−0.751709	+	0.659495i	$0.770770\pi$
$492$	0.697934	0.0314653
$493$	−2.52600	−0.113765
$494$	23.0450	1.03684
$495$	6.91470	0.310793
$496$	−15.3929	−0.691162
$497$	−2.02596	−0.0908765
$498$	−23.2221	−1.04061
$499$	−41.9510	−1.87798	−0.938992	−	0.343939i	$-0.888239\pi$
$499$	−41.9510	−1.87798	−0.938992	+	0.343939i	$0.888239\pi$
$500$	−19.6230	−0.877568
$501$	−22.4536	−1.00315
$502$	−37.0853	−1.65520
$503$	16.9948	0.757762	0.378881	−	0.925445i	$-0.376309\pi$
$503$	16.9948	0.757762	0.378881	+	0.925445i	$0.376309\pi$
$504$	−0.366368	−0.0163193
$505$	25.3320	1.12726
$506$	−4.12442	−0.183353
$507$	18.0815	0.803026
$508$	−28.9110	−1.28272
$509$	−4.23917	−0.187898	−0.0939490	−	0.995577i	$-0.529949\pi$
$509$	−4.23917	−0.187898	−0.0939490	+	0.995577i	$0.529949\pi$
$510$	−7.35729	−0.325786
$511$	16.5771	0.733328
$512$	−31.8743	−1.40866
$513$	−10.6620	−0.470740
$514$	46.6563	2.05792
$515$	−16.4465	−0.724719
$516$	2.03698	0.0896731
$517$	−12.5093	−0.550160
$518$	−2.48084	−0.109002
$519$	−9.76002	−0.428417
$520$	1.06307	0.0466187
$521$	−25.5478	−1.11927	−0.559635	−	0.828739i	$-0.689059\pi$
$521$	−25.5478	−1.11927	−0.559635	+	0.828739i	$0.689059\pi$
$522$	9.73796	0.426219
$523$	−26.5609	−1.16143	−0.580714	−	0.814107i	$-0.697227\pi$
$523$	−26.5609	−1.16143	−0.580714	+	0.814107i	$0.697227\pi$
$524$	−18.6402	−0.814299
$525$	28.2730	1.23393
$526$	19.4346	0.847390
$527$	−3.79764	−0.165428
$528$	−4.18473	−0.182117
$529$	−18.7184	−0.813843
$530$	66.3904	2.88381
$531$	6.65648	0.288867
$532$	14.5319	0.630037
$533$	−1.89266	−0.0819803
$534$	−8.99917	−0.389432
$535$	51.0638	2.20768
$536$	0.301259	0.0130124
$537$	−22.3107	−0.962776
$538$	−39.9848	−1.72387
$539$	5.38365	0.231890
$540$	35.9328	1.54630
$541$	−3.27255	−0.140698	−0.0703490	−	0.997522i	$-0.522411\pi$
$541$	−3.27255	−0.140698	−0.0703490	+	0.997522i	$0.522411\pi$
$542$	20.3072	0.872267
$543$	−0.781279	−0.0335279
$544$	−7.97149	−0.341775
$545$	−15.8786	−0.680167
$546$	40.0028	1.71196
$547$	9.53519	0.407695	0.203848	−	0.979003i	$-0.434655\pi$
$547$	9.53519	0.407695	0.203848	+	0.979003i	$0.434655\pi$
$548$	−4.46123	−0.190574
$549$	2.79034	0.119089
$550$	−15.5112	−0.661399
$551$	5.28695	0.225232
$552$	0.114996	0.00489455
$553$	0.345422	0.0146888
$554$	−13.7537	−0.584337
$555$	−1.30549	−0.0554151
$556$	13.3682	0.566940
$557$	−42.2556	−1.79043	−0.895213	−	0.445639i	$-0.852977\pi$
$557$	−42.2556	−1.79043	−0.895213	+	0.445639i	$0.852977\pi$
$558$	14.6403	0.619772
$559$	−5.52390	−0.233636
$560$	50.9952	2.15494
$561$	−1.03243	−0.0435893
$562$	17.2365	0.727079
$563$	−25.8150	−1.08797	−0.543987	−	0.839094i	$-0.683086\pi$
$563$	−25.8150	−1.08797	−0.543987	+	0.839094i	$0.683086\pi$
$564$	−25.4813	−1.07295
$565$	21.3851	0.899680
$566$	−53.6026	−2.25308
$567$	1.91066	0.0802401
$568$	−0.0309901	−0.00130032
$569$	8.04770	0.337377	0.168689	−	0.985669i	$-0.446047\pi$
$569$	8.04770	0.337377	0.168689	+	0.985669i	$0.446047\pi$
$570$	15.3989	0.644989
$571$	25.6790	1.07463	0.537317	−	0.843381i	$-0.319438\pi$
$571$	25.6790	1.07463	0.537317	+	0.843381i	$0.319438\pi$
$572$	−10.8986	−0.455694
$573$	−6.09497	−0.254621
$574$	−2.40332	−0.100312
$575$	16.1024	0.671515
$576$	15.0521	0.627169
$577$	17.4126	0.724896	0.362448	−	0.932004i	$-0.381941\pi$
$577$	17.4126	0.724896	0.362448	+	0.932004i	$0.381941\pi$
$578$	−1.99324	−0.0829077
$579$	1.82839	0.0759854
$580$	−17.8179	−0.739848
$581$	39.7106	1.64747
$582$	−29.5798	−1.22612
$583$	9.31641	0.385846
$584$	0.253573	0.0104929
$585$	−38.1961	−1.57922
$586$	21.6102	0.892709
$587$	37.6634	1.55453	0.777267	−	0.629171i	$-0.216605\pi$
$587$	37.6634	1.55453	0.777267	+	0.629171i	$0.216605\pi$
$588$	10.9664	0.452246
$589$	7.94851	0.327513
$590$	−24.5259	−1.00972
$591$	7.27650	0.299315
$592$	−1.43358	−0.0589199
$593$	−20.4194	−0.838524	−0.419262	−	0.907865i	$-0.637711\pi$
$593$	−20.4194	−0.838524	−0.419262	+	0.907865i	$0.637711\pi$
$594$	10.1538	0.416614
$595$	12.5812	0.515779
$596$	−33.7950	−1.38430
$597$	3.49199	0.142918
$598$	22.7829	0.931661
$599$	−0.541100	−0.0221088	−0.0110544	−	0.999939i	$-0.503519\pi$
$599$	−0.541100	−0.0221088	−0.0110544	+	0.999939i	$0.503519\pi$
$600$	0.432479	0.0176559
$601$	−29.2501	−1.19314	−0.596568	−	0.802563i	$-0.703469\pi$
$601$	−29.2501	−1.19314	−0.596568	+	0.802563i	$0.703469\pi$
$602$	−7.01428	−0.285881
$603$	−10.8243	−0.440798
$604$	12.4654	0.507208
$605$	−3.57518	−0.145352
$606$	14.5812	0.592320
$607$	6.01733	0.244236	0.122118	−	0.992516i	$-0.461031\pi$
$607$	6.01733	0.244236	0.122118	+	0.992516i	$0.461031\pi$
$608$	16.6844	0.676643
$609$	9.17737	0.371886
$610$	−10.2810	−0.416268
$611$	69.1003	2.79550
$612$	3.81594	0.154250
$613$	−38.6789	−1.56223	−0.781113	−	0.624389i	$-0.785348\pi$
$613$	−38.6789	−1.56223	−0.781113	+	0.624389i	$0.785348\pi$
$614$	16.5182	0.666622
$615$	−1.26470	−0.0509975
$616$	0.189427	0.00763224
$617$	−28.4867	−1.14683	−0.573415	−	0.819265i	$-0.694382\pi$
$617$	−28.4867	−1.14683	−0.573415	+	0.819265i	$0.694382\pi$
$618$	−9.46663	−0.380804
$619$	9.93781	0.399434	0.199717	−	0.979854i	$-0.435998\pi$
$619$	9.93781	0.399434	0.199717	+	0.979854i	$0.435998\pi$
$620$	−26.7878	−1.07583
$621$	−10.5407	−0.422986
$622$	11.4663	0.459758
$623$	15.3889	0.616542
$624$	23.1161	0.925383
$625$	−3.35149	−0.134060
$626$	63.0627	2.52049
$627$	2.16089	0.0862977
$628$	44.2394	1.76534
$629$	−0.353684	−0.0141023
$630$	−48.5017	−1.93235
$631$	−14.0499	−0.559317	−0.279659	−	0.960100i	$-0.590221\pi$
$631$	−14.0499	−0.559317	−0.279659	+	0.960100i	$0.590221\pi$
$632$	0.00528377	0.000210177 0
$633$	−22.2191	−0.883129
$634$	−32.3930	−1.28649
$635$	52.3884	2.07897
$636$	18.9773	0.752500
$637$	−29.7387	−1.17829
$638$	−5.03491	−0.199334
$639$	1.11348	0.0440485
$640$	1.53945	0.0608522
$641$	−42.8295	−1.69166	−0.845832	−	0.533449i	$-0.820896\pi$
$641$	−42.8295	−1.69166	−0.845832	+	0.533449i	$0.820896\pi$
$642$	29.3924	1.16003
$643$	32.2275	1.27093	0.635464	−	0.772131i	$-0.280809\pi$
$643$	32.2275	1.27093	0.635464	+	0.772131i	$0.280809\pi$
$644$	14.3666	0.566123
$645$	−3.69113	−0.145338
$646$	4.17187	0.164140
$647$	−16.7603	−0.658915	−0.329457	−	0.944170i	$-0.606866\pi$
$647$	−16.7603	−0.658915	−0.329457	+	0.944170i	$0.606866\pi$
$648$	0.0292265	0.00114812
$649$	−3.44167	−0.135097
$650$	85.6822	3.36073
$651$	13.7975	0.540765
$652$	−8.68618	−0.340177
$653$	−25.2732	−0.989017	−0.494508	−	0.869173i	$-0.664652\pi$
$653$	−25.2732	−0.989017	−0.494508	+	0.869173i	$0.664652\pi$
$654$	−9.13978	−0.357394
$655$	33.7771	1.31978
$656$	−1.38878	−0.0542229
$657$	−9.11088	−0.355449
$658$	87.7440	3.42062
$659$	−10.9792	−0.427691	−0.213845	−	0.976868i	$-0.568599\pi$
$659$	−10.9792	−0.427691	−0.213845	+	0.976868i	$0.568599\pi$
$660$	−7.28257	−0.283474
$661$	−27.7309	−1.07861	−0.539303	−	0.842112i	$-0.681312\pi$
$661$	−27.7309	−1.07861	−0.539303	+	0.842112i	$0.681312\pi$
$662$	5.91978	0.230079
$663$	5.70305	0.221488
$664$	0.607435	0.0235730
$665$	−26.3326	−1.02113
$666$	1.36349	0.0528340
$667$	5.22681	0.202383
$668$	−42.9093	−1.66021
$669$	−8.78245	−0.339549
$670$	39.8822	1.54078
$671$	−1.44272	−0.0556954
$672$	28.9618	1.11722
$673$	4.84871	0.186904	0.0934521	−	0.995624i	$-0.470210\pi$
$673$	4.84871	0.186904	0.0934521	+	0.995624i	$0.470210\pi$
$674$	−3.51558	−0.135415
$675$	−39.6418	−1.52581
$676$	34.5540	1.32900
$677$	3.97167	0.152644	0.0763218	−	0.997083i	$-0.475682\pi$
$677$	3.97167	0.152644	0.0763218	+	0.997083i	$0.475682\pi$
$678$	12.3093	0.472737
$679$	50.5824	1.94117
$680$	0.192449	0.00738008
$681$	17.0281	0.652518
$682$	−7.56960	−0.289855
$683$	36.0502	1.37942	0.689712	−	0.724084i	$-0.257737\pi$
$683$	36.0502	1.37942	0.689712	+	0.724084i	$0.257737\pi$
$684$	−7.98681	−0.305383
$685$	8.08401	0.308874
$686$	11.3375	0.432870
$687$	17.9286	0.684017
$688$	−4.05328	−0.154530
$689$	−51.4629	−1.96058
$690$	15.2237	0.579558
$691$	18.1778	0.691515	0.345757	−	0.938324i	$-0.387622\pi$
$691$	18.1778	0.691515	0.345757	+	0.938324i	$0.387622\pi$
$692$	−18.6516	−0.709027
$693$	−6.80613	−0.258543
$694$	−9.14386	−0.347096
$695$	−24.2240	−0.918870
$696$	0.140382	0.00532117
$697$	−0.342632	−0.0129781
$698$	−8.44126	−0.319507
$699$	16.6188	0.628580
$700$	54.0301	2.04215
$701$	11.1086	0.419568	0.209784	−	0.977748i	$-0.432724\pi$
$701$	11.1086	0.419568	0.209784	+	0.977748i	$0.432724\pi$
$702$	−56.0883	−2.11692
$703$	0.740266	0.0279197
$704$	−7.78251	−0.293315
$705$	46.1735	1.73900
$706$	24.8682	0.935928
$707$	−24.9343	−0.937750
$708$	−7.01061	−0.263475
$709$	10.7001	0.401849	0.200925	−	0.979607i	$-0.435605\pi$
$709$	10.7001	0.401849	0.200925	+	0.979607i	$0.435605\pi$
$710$	−4.10263	−0.153969
$711$	−0.189846	−0.00711979
$712$	0.235397	0.00882186
$713$	7.85810	0.294288
$714$	7.24176	0.271016
$715$	19.7489	0.738568
$716$	−42.6361	−1.59338
$717$	−11.6524	−0.435165
$718$	−16.0139	−0.597633
$719$	−19.2420	−0.717607	−0.358803	−	0.933413i	$-0.616815\pi$
$719$	−19.2420	−0.717607	−0.358803	+	0.933413i	$0.616815\pi$
$720$	−28.0273	−1.04451
$721$	16.1882	0.602882
$722$	29.1397	1.08447
$723$	8.81937	0.327996
$724$	−1.49304	−0.0554883
$725$	19.6571	0.730046
$726$	−2.05788	−0.0763751
$727$	−22.7996	−0.845589	−0.422795	−	0.906225i	$-0.638951\pi$
$727$	−22.7996	−0.845589	−0.422795	+	0.906225i	$0.638951\pi$
$728$	−1.04638	−0.0387813
$729$	14.7278	0.545475
$730$	33.5692	1.24245
$731$	−1.00000	−0.0369863
$732$	−2.93878	−0.108621
$733$	34.2926	1.26663	0.633314	−	0.773895i	$-0.281694\pi$
$733$	34.2926	1.26663	0.633314	+	0.773895i	$0.281694\pi$
$734$	42.7664	1.57854
$735$	−19.8717	−0.732979
$736$	16.4947	0.608001
$737$	5.59658	0.206153
$738$	1.32088	0.0486221
$739$	−37.8704	−1.39309	−0.696543	−	0.717515i	$-0.745279\pi$
$739$	−37.8704	−1.39309	−0.696543	+	0.717515i	$0.745279\pi$
$740$	−2.49482	−0.0917114
$741$	−11.9365	−0.438500
$742$	−65.3479	−2.39900
$743$	−37.2519	−1.36664	−0.683319	−	0.730120i	$-0.739464\pi$
$743$	−37.2519	−1.36664	−0.683319	+	0.730120i	$0.739464\pi$
$744$	0.211054	0.00773760
$745$	61.2385	2.24361
$746$	13.0330	0.477173
$747$	−21.8252	−0.798541
$748$	−1.97299	−0.0721398
$749$	−50.2620	−1.83653
$750$	20.4673	0.747359
$751$	7.01597	0.256016	0.128008	−	0.991773i	$-0.459142\pi$
$751$	7.01597	0.256016	0.128008	+	0.991773i	$0.459142\pi$
$752$	50.7039	1.84898
$753$	19.2090	0.700013
$754$	27.8124	1.01287
$755$	−22.5880	−0.822060
$756$	−35.3686	−1.28634
$757$	−49.7525	−1.80828	−0.904142	−	0.427232i	$-0.859489\pi$
$757$	−49.7525	−1.80828	−0.904142	+	0.427232i	$0.859489\pi$
$758$	17.5552	0.637635
$759$	2.13631	0.0775432
$760$	−0.402798	−0.0146110
$761$	−6.16264	−0.223396	−0.111698	−	0.993742i	$-0.535629\pi$
$761$	−6.16264	−0.223396	−0.111698	+	0.993742i	$0.535629\pi$
$762$	30.1549	1.09240
$763$	15.6293	0.565819
$764$	−11.6476	−0.421395
$765$	−6.91470	−0.250002
$766$	73.9669	2.67253
$767$	19.0114	0.686463
$768$	16.9559	0.611844
$769$	−17.5637	−0.633362	−0.316681	−	0.948532i	$-0.602568\pi$
$769$	−17.5637	−0.633362	−0.316681	+	0.948532i	$0.602568\pi$
$770$	25.0773	0.903724
$771$	−24.1664	−0.870332
$772$	3.49409	0.125755
$773$	−43.3619	−1.55962	−0.779809	−	0.626018i	$-0.784684\pi$
$773$	−43.3619	−1.55962	−0.779809	+	0.626018i	$0.784684\pi$
$774$	3.85509	0.138568
$775$	29.5529	1.06157
$776$	0.773736	0.0277755
$777$	1.28499	0.0460989
$778$	−27.4362	−0.983636
$779$	0.717132	0.0256939
$780$	40.2282	1.44040
$781$	−0.575712	−0.0206006
$782$	4.12442	0.147489
$783$	−12.8677	−0.459854
$784$	−21.8214	−0.779337
$785$	−80.1643	−2.86119
$786$	19.4421	0.693478
$787$	−14.6458	−0.522066	−0.261033	−	0.965330i	$-0.584063\pi$
$787$	−14.6458	−0.522066	−0.261033	+	0.965330i	$0.584063\pi$
$788$	13.9055	0.495364
$789$	−10.0665	−0.358377
$790$	0.699492	0.0248868
$791$	−21.0493	−0.748429
$792$	−0.104110	−0.00369940
$793$	7.96942	0.283002
$794$	−26.5411	−0.941908
$795$	−34.3880	−1.21962
$796$	6.67326	0.236527
$797$	43.0799	1.52597	0.762985	−	0.646417i	$-0.223733\pi$
$797$	43.0799	1.52597	0.762985	+	0.646417i	$0.223733\pi$
$798$	−15.1571	−0.536556
$799$	12.5093	0.442548
$800$	62.0334	2.19321
$801$	−8.45781	−0.298842
$802$	−37.5107	−1.32455
$803$	4.71069	0.166237
$804$	11.4001	0.402051
$805$	−26.0331	−0.917546
$806$	41.8137	1.47283
$807$	20.7108	0.729056
$808$	−0.381408	−0.0134179
$809$	25.5258	0.897439	0.448720	−	0.893673i	$-0.351880\pi$
$809$	25.5258	0.897439	0.448720	+	0.893673i	$0.351880\pi$
$810$	3.86915	0.135948
$811$	−4.76135	−0.167194	−0.0835968	−	0.996500i	$-0.526641\pi$
$811$	−4.76135	−0.167194	−0.0835968	+	0.996500i	$0.526641\pi$
$812$	17.5381	0.615468
$813$	−10.5184	−0.368898
$814$	−0.704977	−0.0247094
$815$	15.7399	0.551343
$816$	4.18473	0.146495
$817$	2.09301	0.0732252
$818$	−61.0769	−2.13550
$819$	37.5964	1.31372
$820$	−2.41686	−0.0844003
$821$	−23.3561	−0.815132	−0.407566	−	0.913176i	$-0.633622\pi$
$821$	−23.3561	−0.815132	−0.407566	+	0.913176i	$0.633622\pi$
$822$	4.65317	0.162298
$823$	−40.2820	−1.40414	−0.702072	−	0.712106i	$-0.747741\pi$
$823$	−40.2820	−1.40414	−0.702072	+	0.712106i	$0.747741\pi$
$824$	0.247624	0.00862640
$825$	8.03428	0.279718
$826$	24.1408	0.839967
$827$	−24.0825	−0.837430	−0.418715	−	0.908118i	$-0.637519\pi$
$827$	−24.0825	−0.837430	−0.418715	+	0.908118i	$0.637519\pi$
$828$	−7.89596	−0.274404
$829$	−5.86422	−0.203673	−0.101836	−	0.994801i	$-0.532472\pi$
$829$	−5.86422	−0.203673	−0.101836	+	0.994801i	$0.532472\pi$
$830$	80.4153	2.79125
$831$	7.12394	0.247127
$832$	42.9898	1.49040
$833$	−5.38365	−0.186532
$834$	−13.9434	−0.482821
$835$	77.7540	2.69079
$836$	4.12950	0.142822
$837$	−19.3456	−0.668681
$838$	−35.4025	−1.22296
$839$	−15.8198	−0.546162	−0.273081	−	0.961991i	$-0.588043\pi$
$839$	−15.8198	−0.546162	−0.273081	+	0.961991i	$0.588043\pi$
$840$	−0.699199	−0.0241247
$841$	−22.6193	−0.779977
$842$	−13.0760	−0.450627
$843$	−8.92795	−0.307495
$844$	−42.4611	−1.46157
$845$	−62.6138	−2.15398
$846$	−48.2246	−1.65800
$847$	3.51904	0.120916
$848$	−37.7620	−1.29675
$849$	27.7644	0.952871
$850$	15.5112	0.532029
$851$	0.731845	0.0250873
$852$	−1.17271	−0.0401765
$853$	−7.58144	−0.259583	−0.129792	−	0.991541i	$-0.541431\pi$
$853$	−7.58144	−0.259583	−0.129792	+	0.991541i	$0.541431\pi$
$854$	10.1196	0.346286
$855$	14.4726	0.494951
$856$	−0.768836	−0.0262783
$857$	42.4249	1.44921	0.724604	−	0.689165i	$-0.242023\pi$
$857$	42.4249	1.44921	0.724604	+	0.689165i	$0.242023\pi$
$858$	11.3675	0.388081
$859$	5.70433	0.194629	0.0973147	−	0.995254i	$-0.468975\pi$
$859$	5.70433	0.194629	0.0973147	+	0.995254i	$0.468975\pi$
$860$	−7.05381	−0.240533
$861$	1.24484	0.0424240
$862$	−15.1380	−0.515601
$863$	6.96738	0.237172	0.118586	−	0.992944i	$-0.462164\pi$
$863$	6.96738	0.237172	0.118586	+	0.992944i	$0.462164\pi$
$864$	−40.6076	−1.38150
$865$	33.7977	1.14916
$866$	35.9902	1.22300
$867$	1.03243	0.0350632
$868$	26.3672	0.894961
$869$	0.0981581	0.00332978
$870$	18.5845	0.630074
$871$	−30.9149	−1.04751
$872$	0.239075	0.00809609
$873$	−27.8004	−0.940900
$874$	−8.63246	−0.291997
$875$	−34.9997	−1.18321
$876$	9.59558	0.324205
$877$	−17.9063	−0.604653	−0.302326	−	0.953204i	$-0.597763\pi$
$877$	−17.9063	−0.604653	−0.302326	+	0.953204i	$0.597763\pi$
$878$	−2.27348	−0.0767261
$879$	−11.1934	−0.377543
$880$	14.4912	0.488499
$881$	−1.11651	−0.0376163	−0.0188081	−	0.999823i	$-0.505987\pi$
$881$	−1.11651	−0.0376163	−0.0188081	+	0.999823i	$0.505987\pi$
$882$	20.7545	0.698839
$883$	−39.2644	−1.32135	−0.660676	−	0.750671i	$-0.729730\pi$
$883$	−39.2644	−1.32135	−0.660676	+	0.750671i	$0.729730\pi$
$884$	10.8986	0.366560
$885$	12.7036	0.427028
$886$	−17.8594	−0.599999
$887$	−42.3253	−1.42115	−0.710573	−	0.703624i	$-0.751564\pi$
$887$	−42.3253	−1.42115	−0.710573	+	0.703624i	$0.751564\pi$
$888$	0.0196560	0.000659612 0
$889$	−51.5658	−1.72946
$890$	31.1630	1.04459
$891$	0.542949	0.0181895
$892$	−16.7834	−0.561951
$893$	−26.1822	−0.876154
$894$	35.2490	1.17890
$895$	77.2590	2.58248
$896$	−1.51528	−0.0506219
$897$	−11.8008	−0.394016
$898$	58.0284	1.93643
$899$	9.59284	0.319939
$900$	−29.6953	−0.989843
$901$	−9.31641	−0.310374
$902$	−0.682946	−0.0227396
$903$	3.63317	0.120904
$904$	−0.321982	−0.0107090
$905$	2.70547	0.0899329
$906$	−13.0017	−0.431952
$907$	−35.5113	−1.17913	−0.589567	−	0.807720i	$-0.700701\pi$
$907$	−35.5113	−1.17913	−0.589567	+	0.807720i	$0.700701\pi$
$908$	32.5410	1.07991
$909$	13.7040	0.454534
$910$	−138.525	−4.59205
$911$	−1.60881	−0.0533023	−0.0266511	−	0.999645i	$-0.508484\pi$
$911$	−1.60881	−0.0533023	−0.0266511	+	0.999645i	$0.508484\pi$
$912$	−8.75870	−0.290030
$913$	11.2845	0.373462
$914$	−77.9561	−2.57856
$915$	5.32524	0.176047
$916$	34.2618	1.13204
$917$	−33.2467	−1.09790
$918$	−10.1538	−0.335124
$919$	−15.6972	−0.517803	−0.258902	−	0.965904i	$-0.583361\pi$
$919$	−15.6972	−0.517803	−0.258902	+	0.965904i	$0.583361\pi$
$920$	−0.398217	−0.0131288
$921$	−8.55590	−0.281926
$922$	−8.29492	−0.273179
$923$	3.18018	0.104677
$924$	7.16822	0.235817
$925$	2.75234	0.0904963
$926$	25.2263	0.828986
$927$	−8.89716	−0.292221
$928$	20.1360	0.660996
$929$	30.7404	1.00856	0.504280	−	0.863540i	$-0.331758\pi$
$929$	30.7404	1.00856	0.504280	+	0.863540i	$0.331758\pi$
$930$	27.9403	0.916200
$931$	11.2680	0.369295
$932$	31.7588	1.04029
$933$	−5.93918	−0.194440
$934$	25.4947	0.834212
$935$	3.57518	0.116921
$936$	0.575095	0.0187976
$937$	4.69986	0.153538	0.0767688	−	0.997049i	$-0.475540\pi$
$937$	4.69986	0.153538	0.0767688	+	0.997049i	$0.475540\pi$
$938$	−39.2560	−1.28175
$939$	−32.6644	−1.06596
$940$	88.2384	2.87802
$941$	19.2659	0.628049	0.314024	−	0.949415i	$-0.398323\pi$
$941$	19.2659	0.628049	0.314024	+	0.949415i	$0.398323\pi$
$942$	−46.1427	−1.50341
$943$	0.708975	0.0230874
$944$	13.9501	0.454036
$945$	64.0899	2.08485
$946$	−1.99324	−0.0648057
$947$	16.6031	0.539528	0.269764	−	0.962926i	$-0.413054\pi$
$947$	16.6031	0.539528	0.269764	+	0.962926i	$0.413054\pi$
$948$	0.199946	0.00649395
$949$	−26.0214	−0.844690
$950$	−32.4651	−1.05331
$951$	16.7785	0.544080
$952$	−0.189427	−0.00613937
$953$	−18.6200	−0.603160	−0.301580	−	0.953441i	$-0.597514\pi$
$953$	−18.6200	−0.603160	−0.301580	+	0.953441i	$0.597514\pi$
$954$	35.9156	1.16281
$955$	21.1061	0.682977
$956$	−22.2679	−0.720194
$957$	2.60792	0.0843021
$958$	23.6313	0.763493
$959$	−7.95708	−0.256947
$960$	28.7262	0.927135
$961$	−16.5779	−0.534772
$962$	3.89422	0.125555
$963$	27.6243	0.890181
$964$	16.8540	0.542830
$965$	−6.33149	−0.203818
$966$	−14.9847	−0.482125
$967$	−40.5306	−1.30337	−0.651687	−	0.758488i	$-0.725939\pi$
$967$	−40.5306	−1.30337	−0.651687	+	0.758488i	$0.725939\pi$
$968$	0.0538292	0.00173014
$969$	−2.16089	−0.0694178
$970$	102.431	3.28886
$971$	−57.1809	−1.83502	−0.917512	−	0.397709i	$-0.869806\pi$
$971$	−57.1809	−1.83502	−0.917512	+	0.397709i	$0.869806\pi$
$972$	31.2579	1.00260
$973$	23.8437	0.764393
$974$	31.2176	1.00028
$975$	−44.3806	−1.42132
$976$	5.84773	0.187181
$977$	4.00052	0.127988	0.0639941	−	0.997950i	$-0.479616\pi$
$977$	4.00052	0.127988	0.0639941	+	0.997950i	$0.479616\pi$
$978$	9.05989	0.289703
$979$	4.37303	0.139763
$980$	−37.9752	−1.21307
$981$	−8.58997	−0.274257
$982$	66.4018	2.11897
$983$	10.7325	0.342314	0.171157	−	0.985244i	$-0.445249\pi$
$983$	10.7325	0.342314	0.171157	+	0.985244i	$0.445249\pi$
$984$	0.0190417	0.000607028 0
$985$	−25.1976	−0.802863
$986$	5.03491	0.160344
$987$	−45.4485	−1.44664
$988$	−22.8110	−0.725713
$989$	2.06921	0.0657969
$990$	−13.7826	−0.438041
$991$	−43.4345	−1.37974	−0.689871	−	0.723933i	$-0.742333\pi$
$991$	−43.4345	−1.37974	−0.689871	+	0.723933i	$0.742333\pi$
$992$	30.2729	0.961165
$993$	−3.06625	−0.0973045
$994$	4.03821	0.128084
$995$	−12.0923	−0.383353
$996$	22.9863	0.728348
$997$	5.08344	0.160994	0.0804971	−	0.996755i	$-0.474349\pi$
$997$	5.08344	0.160994	0.0804971	+	0.996755i	$0.474349\pi$
$998$	83.6182	2.64689
$999$	−1.80170	−0.0570034

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8041.2.a.d.1.11	✓	62

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8041.2.a.d.1.11	✓	62	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 8041 = 11 \cdot 17 \cdot 43 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8041.a (trivial)

\(f(q)\)	\(=\)	\(q-1.99324 q^{2} +1.03243 q^{3} +1.97299 q^{4} -3.57518 q^{5} -2.05788 q^{6} +3.51904 q^{7} +0.0538292 q^{8} -1.93409 q^{9} +O(q^{10})\)	\(q-1.99324 q^{2} +1.03243 q^{3} +1.97299 q^{4} -3.57518 q^{5} -2.05788 q^{6} +3.51904 q^{7} +0.0538292 q^{8} -1.93409 q^{9} +7.12618 q^{10} +1.00000 q^{11} +2.03698 q^{12} -5.52390 q^{13} -7.01428 q^{14} -3.69113 q^{15} -4.05328 q^{16} -1.00000 q^{17} +3.85509 q^{18} +2.09301 q^{19} -7.05381 q^{20} +3.63317 q^{21} -1.99324 q^{22} +2.06921 q^{23} +0.0555749 q^{24} +7.78190 q^{25} +11.0104 q^{26} -5.09410 q^{27} +6.94305 q^{28} +2.52600 q^{29} +7.35729 q^{30} +3.79764 q^{31} +7.97149 q^{32} +1.03243 q^{33} +1.99324 q^{34} -12.5812 q^{35} -3.81594 q^{36} +0.353684 q^{37} -4.17187 q^{38} -5.70305 q^{39} -0.192449 q^{40} +0.342632 q^{41} -7.24176 q^{42} +1.00000 q^{43} +1.97299 q^{44} +6.91470 q^{45} -4.12442 q^{46} -12.5093 q^{47} -4.18473 q^{48} +5.38365 q^{49} -15.5112 q^{50} -1.03243 q^{51} -10.8986 q^{52} +9.31641 q^{53} +10.1538 q^{54} -3.57518 q^{55} +0.189427 q^{56} +2.16089 q^{57} -5.03491 q^{58} -3.44167 q^{59} -7.28257 q^{60} -1.44272 q^{61} -7.56960 q^{62} -6.80613 q^{63} -7.78251 q^{64} +19.7489 q^{65} -2.05788 q^{66} +5.59658 q^{67} -1.97299 q^{68} +2.13631 q^{69} +25.0773 q^{70} -0.575712 q^{71} -0.104110 q^{72} +4.71069 q^{73} -0.704977 q^{74} +8.03428 q^{75} +4.12950 q^{76} +3.51904 q^{77} +11.3675 q^{78} +0.0981581 q^{79} +14.4912 q^{80} +0.542949 q^{81} -0.682946 q^{82} +11.2845 q^{83} +7.16822 q^{84} +3.57518 q^{85} -1.99324 q^{86} +2.60792 q^{87} +0.0538292 q^{88} +4.37303 q^{89} -13.7826 q^{90} -19.4388 q^{91} +4.08253 q^{92} +3.92080 q^{93} +24.9341 q^{94} -7.48289 q^{95} +8.23002 q^{96} +14.3739 q^{97} -10.7309 q^{98} -1.93409 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9}+O(q^{10}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9	\( 62 q - 7 q^{2} - 8 q^{3} + 49 q^{4} - 13 q^{5} - 2 q^{6} - 11 q^{7} - 9 q^{8} + 40 q^{9} - 7 q^{10} + 62 q^{11} - 17 q^{12} - 31 q^{14} - 20 q^{15} + 27 q^{16} - 62 q^{17} + 3 q^{18} - 29 q^{20} - 18 q^{21} - 7 q^{22} - 50 q^{23} - 31 q^{24} + 35 q^{25} - 32 q^{26} - 14 q^{27} - 13 q^{28} - 26 q^{29} - 10 q^{30} - 58 q^{31} - 5 q^{32} - 8 q^{33} + 7 q^{34} - 32 q^{35} - 29 q^{36} - 41 q^{37} - 10 q^{38} - 53 q^{39} - 31 q^{40} - 55 q^{41} - 7 q^{42} + 62 q^{43} + 49 q^{44} - 34 q^{45} - 39 q^{46} - 31 q^{47} - 30 q^{48} + 35 q^{49} - 40 q^{50} + 8 q^{51} + 13 q^{52} - 74 q^{53} + 48 q^{54} - 13 q^{55} - 75 q^{56} - 43 q^{57} - 46 q^{58} - 65 q^{59} - 8 q^{60} - 14 q^{61} - 29 q^{62} - 23 q^{63} - 15 q^{64} - 9 q^{65} - 2 q^{66} - q^{67} - 49 q^{68} - 59 q^{69} - 31 q^{70} - 141 q^{71} + 9 q^{72} - 4 q^{73} - 94 q^{74} - 43 q^{75} + 34 q^{76} - 11 q^{77} - 11 q^{78} - 63 q^{79} - 41 q^{80} - 30 q^{81} + 38 q^{82} - 44 q^{83} - 16 q^{84} + 13 q^{85} - 7 q^{86} - 8 q^{87} - 9 q^{88} - 58 q^{89} - 55 q^{90} - 78 q^{91} - 104 q^{92} - 5 q^{94} - 99 q^{95} - 148 q^{96} - 26 q^{97} + 16 q^{98} + 40 q^{99}+O(q^{100}) \) 62 * q - 7 * q^2 - 8 * q^3 + 49 * q^4 - 13 * q^5 - 2 * q^6 - 11 * q^7 - 9 * q^8 + 40 * q^9 - 7 * q^10 + 62 * q^11 - 17 * q^12 - 31 * q^14 - 20 * q^15 + 27 * q^16 - 62 * q^17 + 3 * q^18 - 29 * q^20 - 18 * q^21 - 7 * q^22 - 50 * q^23 - 31 * q^24 + 35 * q^25 - 32 * q^26 - 14 * q^27 - 13 * q^28 - 26 * q^29 - 10 * q^30 - 58 * q^31 - 5 * q^32 - 8 * q^33 + 7 * q^34 - 32 * q^35 - 29 * q^36 - 41 * q^37 - 10 * q^38 - 53 * q^39 - 31 * q^40 - 55 * q^41 - 7 * q^42 + 62 * q^43 + 49 * q^44 - 34 * q^45 - 39 * q^46 - 31 * q^47 - 30 * q^48 + 35 * q^49 - 40 * q^50 + 8 * q^51 + 13 * q^52 - 74 * q^53 + 48 * q^54 - 13 * q^55 - 75 * q^56 - 43 * q^57 - 46 * q^58 - 65 * q^59 - 8 * q^60 - 14 * q^61 - 29 * q^62 - 23 * q^63 - 15 * q^64 - 9 * q^65 - 2 * q^66 - q^67 - 49 * q^68 - 59 * q^69 - 31 * q^70 - 141 * q^71 + 9 * q^72 - 4 * q^73 - 94 * q^74 - 43 * q^75 + 34 * q^76 - 11 * q^77 - 11 * q^78 - 63 * q^79 - 41 * q^80 - 30 * q^81 + 38 * q^82 - 44 * q^83 - 16 * q^84 + 13 * q^85 - 7 * q^86 - 8 * q^87 - 9 * q^88 - 58 * q^89 - 55 * q^90 - 78 * q^91 - 104 * q^92 - 5 * q^94 - 99 * q^95 - 148 * q^96 - 26 * q^97 + 16 * q^98 + 40 * q^99

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